A Kiefer-Wolfowitz theorem for convex densities

DOI10.1214/074921707000000256zbMath1176.62051arXivmath/0701179OpenAlexW1596827873MaRDI QIDQ5324529

Jon A. Wellner, Fadoua Balabdaoui

Publication date: 3 August 2009

Published in: Institute of Mathematical Statistics Lecture Notes - Monograph Series (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0701179

zbMATH Keywords

distanceBrownian bridgeempirical distributionshape constraintsmonotone densityinvelope processoptimality theory

Mathematics Subject Classification ID

Nonparametric hypothesis testing (62G10) Asymptotic properties of nonparametric inference (62G20) Central limit and other weak theorems (60F05) Order statistics; empirical distribution functions (62G30)

Related Items (8)

Estimation of a distribution function with increasing failure rate average ⋮ Maximum likelihood estimation of a log-concave density and its distribution function: basic properties and uniform consistency ⋮ A Kiefer-Wolfowitz type of result in a general setting, with an application to smooth monotone estimation ⋮ Uniform central limit theorems for the Grenander estimator ⋮ A second Marshall inequality in convex estimation ⋮ Refinements of the Kiefer-Wolfowitz theorem and a test of concavity ⋮ An exponential inequality for the distribution function of the kernel density estimator, with applications to adaptive estimation ⋮ Marshall lemma in discrete convex estimation

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